Amazing Graze

Time Limit : 1 sec, Memory Limit : 65536 KB
Japanese version is here

Problem E: Amazing Graze

In 2215 A.D., a war between two planets, ACM and ICPC, is being more and more intense.

ACM introduced new combat planes. These planes have a special system that is called Graze, and fighting power of a plane increases when it is close to energy bullets that ICPC combat planes shoot.

Both combat planes and energy bullets have a shape of a sphere with a radius of R. Precisely, fighting power of a plane is equivalent to the number of energy bullet where distance from the plane is less than or equals to 2R.

You, helper of captain of intelligence units, are asked to analyze a war situation. The information given to you is coordinates of AN combat planes and BN energy bullets. Additionally, you know following things:

  • All combat planes and energy bullet has same z-coordinates. In other word, z-coordinate can be ignored.
  • No two combat planes, no two energy bullets, and no pair of combat plane and energy bullet collide (i.e. have positive common volume) each other.

Your task is to write a program that outputs total fighting power of all combat planes.

Input

Input file consists of a number of data sets. One data set is given in following format:

AN BN R
XA1 YA1
XA2 YA2
:
XAAN YAAN
XB1 YB1
XB2 YB2
:
XBBN YBBN

AN, BN, R are integers that describe the number of combat planes, energy bullets, and their radius respectively.

Following AN lines indicate coordinates of the center of combat planes. Each line has two integers that describe x-coordinate and y-coordinate.

Following BN lines indicate coordinates of the center of energy bullets, in the same format as that of combat planes.

Input ends when AN = BN = 0. You should output nothing for this case.

Output

For each data set, output the total fighting power.

Constraints

  • Jude data includes at most 20 data sets.
  • 1 ≤ AN, BN ≤ 100000
  • 0 < R ≤ 10
  • 0 ≤ (coordinate values) < 10000

Sample Input

2 2 1
0 0
0 4
2 2
2 8
0 0 0

Output for the Sample Input

2

Source: University of Aizu Programming Contest , Aizu-Wakamatsu, Japan, 2009-03-28
Problem Setter:  Takashi Tayama